Incorrect.
Tattoos can cause serious illness from contamination. Sometimes these illnesses do not show up till later. This can cause the individual to not be deploy-able.
Tattoos can be of a nature to be disruptive to the good order and conduct of the Army. An example of this would be an Aryan Nation or NAZI tattoo. Such tattoos can seriously disrupt unit cohesion.
Additionally, tattoos that are not viewed in the US as being offensive, can be very offensive to other nations where the individual is deployed. Crosses or Stars of David can lead to big problems with host countries.
If done correctly, tattoos are safe with no infections almost 100% of the time. It's not rocket science.
Tattoos can be of a nature to be disruptive to the good order and conduct of the Army.
Someone should tell that to the Army. They've had tattooed soldiers for decades.
An example of this would be an Aryan Nation or NAZI tattoo.
Those tattoos are not permitted, and still won't be permitted, under these changes.